Answer:
300 cars must be made to minimize the unit cost
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a>0, the vertex is a minimum point, that is, the minimum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
The cost of producing x cars is given by:
[tex]C(x) = 0.7x^2 - 420x + 81610[/tex]
So a quadratic equation with [tex]a = 0.7, b = -420, c = 81610[/tex]
How many cars must be made to minimize the unit cost?
This is the xvalue of the vertex. So
[tex]x_v = -\frac{b}{2a} = -\frac{-420}{2*0.7} = \frac{420}{1.4} = 300[/tex]
300 cars must be made to minimize the unit cost
